In this contribution High-Performance Computing electromagnetic methods are applied to the design of a patch antenna combined with EBG structure in order to obtain bandwidth enhancement. The electrical characteristics of the embedded structure (patch antenna surrounded by EBG unit cells) are evaluated by means of Method of Moment technique (MoM) whereas for designing the unit cell, the Finite Element Method (FEM) together with the Bloch-Floquet theory is used. The manufactured prototypes are characterized in terms of return loss and radiation pattern in an anechoic chamber.